Toast the pine nuts. Place the 1/3 cup of pine nuts in a small, dry skillet over medium-low heat. Toast for 3-5 minutes, tossing frequently, until golden brown and fragrant. Watch them carefully as they can burn quickly. Remove from the skillet and set aside to cool.

Combine pesto ingredients. In the bowl of a food processor, combine the fresh basil, toasted pine nuts, grated Parmigiano-Reggiano, and chopped garlic. Pulse several times until the ingredients are finely minced.

Add the olive oil. With the food processor running on low, slowly stream in the extra virgin olive oil until the mixture is smooth and emulsified.

Season the pesto. Scrape down the sides of the bowl. Add the lemon juice, sea salt, and black pepper. Pulse a few more times to combine. Taste and adjust seasoning if necessary. Set aside.

Cook the pasta. Bring a large pot of water to a rolling boil. Add the 1 tbsp of kosher salt, then add the pasta. Cook according to package directions until al dente (firm to the bite).

Reserve pasta water. Just before draining the pasta, carefully scoop out about 1 cup of the starchy pasta water and set it aside. This is the key to a creamy sauce.

Combine pasta and pesto. Drain the pasta in a colander. Do not rinse. Return the hot, drained pasta to the pot or transfer to a large mixing bowl. Immediately add the prepared pesto and toss to coat the pasta thoroughly.

Create the sauce. Add 1/4 cup of the reserved pasta water and stir vigorously. The starch in the water will help the pesto cling to the pasta and create a creamy sauce. Add more pasta water, one tablespoon at a time, until you reach your desired sauce consistency.

Serve. Divide the pesto pasta among serving plates. Garnish with extra grated Parmigiano-Reggiano, a few extra toasted pine nuts, and a sprig of fresh basil. Serve immediately.